Question

watch the video and then solve the problem given below. click here to watch the video. the formula p = 0.01a² + 0.05a + 107 models a womans normal systolic blood - pressure, p, at age a. use this formula to find the age, to the nearest year, of a woman whose normal systolic blood pressure is 140 mm hg. enter the age in years. (round to the nearest whole number as needed.)

Explanation:

Step1: Set up the equation

We are given the formula $P = 0.01A^{2}+0.05A + 107$ and $P = 140$. So, we set up the equation $0.01A^{2}+0.05A + 107=140$.

Step2: Rearrange the equation

Subtract 140 from both sides to get a quadratic - equation in standard form: $0.01A^{2}+0.05A+107 - 140 = 0$, which simplifies to $0.01A^{2}+0.05A - 33 = 0$. Multiply through by 100 to clear the decimals: $A^{2}+5A - 3300 = 0$.

Step3: Use the quadratic formula

The quadratic formula for a quadratic equation $ax^{2}+bx + c = 0$ is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For $A^{2}+5A - 3300 = 0$, we have $a = 1$, $b = 5$, and $c=-3300$. First, calculate the discriminant $\Delta=b^{2}-4ac=(5)^{2}-4\times1\times(-3300)=25 + 13200 = 13225$.

Step4: Find the values of A

$A=\frac{-5\pm\sqrt{13225}}{2}=\frac{-5\pm115}{2}$. We have two solutions: $A_1=\frac{-5 + 115}{2}=\frac{110}{2}=55$ and $A_2=\frac{-5 - 115}{2}=\frac{-120}{2}=-60$. Since age cannot be negative, we reject the negative solution.

Answer:

55